Quadrature Amplitude Modulation (QAM), Phase Shift Keying (PSK), Binary PSK (BPSK), and Quadrature PSK (QPSK) are some of the commonly used modulation techniques in digital communication systems. The set of all symbols and their arrangement in a modulation technique is referred as a “constellation.”
In general, the reference phase and amplitude of the modulation constellation are required at the receiver to estimate the symbols sent by the transmitter. In general, the phase and amplitude of the constellation show random variations due to variety of channel impairments such as fading, frequency response of the channel, frequency offset, timing offset, etc. In coherent detection, the reference phase and amplitude of the modulation constellation may be obtained from reference symbols that may be transmitted along with the data symbols. In non-coherent detection, previously detected symbols may be used as reference symbols for detecting current symbols. In general, coherent detection provides superior performance than non-coherent detection. The overhead in terms of the bandwidth and power allocated for transmitting reference symbols is justified by the improved performance. The process of estimating the phase and amplitude of the channel to demodulate the symbol received on the channel is referred to as channel estimation. The process of compensating the effect of the random phase and amplitude variation by using the estimated channel conditions is referred to as equalization.
Orthogonal frequency division multiplexing (OFDM) is a multi-carrier modulation scheme used in many digital communication systems. In OFDM, a large number of closely spaced orthogonal subcarriers are used to transmit data as shown in FIG. 1. The data are divided into several parallel data streams, one for each subcarrier. Each subcarrier is modulated with a conventional modulation scheme such as QAM, PSK, BPSK, or QPSK, at a low symbol rate while maintaining total data rate similar to single carrier modulation schemes in the same channel bandwidth. The frequency spacing between two adjacent subcarriers is referred as subcarrier spacing and it is denoted by Δf. The rate at which the individual subcarriers are modulated is referred as symbol rate. The collection of all the subcarriers is referred as an OFDM symbol. The OFDM symbol rate is the same as the data symbol rate on each individual subcarrier. The OFDM symbol duration is denoted by Tu. The OFDM signal is typically generated in frequency domain and then converted in time domain. An OFDM signal over one symbol duration is referred as an OFDM symbol in both time domain and frequency domain. Additional details about OFDM may be found in “3G Evolution: HSPA and LTE for Mobile Broadband” by Dahlman, Parkvall, Sköld and Beming, published by Academic Press, 1st Edition© 2007, the entire disclosure of which is hereby expressly incorporated by reference herein.
The primary advantage of OFDM over single carrier modulation schemes is its ability to cope with severe channel conditions such as attenuation of high frequencies in a channel, narrowband interference and frequency selective fading due to multipath without requiring complex equalization filters. Channel equalization is simplified because OFDM may be viewed as using many slowly modulated narrowband signals rather than one rapidly modulated wideband signal. The low symbol rate makes the use of a guard interval between OFDM symbols affordable, making it possible to handle time spreading and eliminate intersymbol interference (ISI).
Low complexity implementation by means of computationally efficient Fast Fourier Transform (FFT) is possible for OFDM due to its specific structure and the selection of a subcarrier spacing Δf equal to the reciprocal of OFDM symbol rate Tu.
An uncorrupted OFDM signal can be demodulated without any interference between subcarriers. The subcarrier orthogonality is due to the fact that a modulated subcarrier consists of an integer number of periods of complex exponentials during the OFDM symbol interval Tu=1/Δf. However, in case of a time dispersive channel the orthogonality between the subcarriers may be lost. The reason for this loss of subcarrier orthogonality is that the OFDM symbol boundary for one path will overlap with the symbol boundary of a different path, as illustrated in FIG. 2. As a consequence, in case of a time dispersive channel there will be intersymbol interference within a subcarrier and interference between subcarriers.
Cyclic prefix insertion is typically used in OFDM to address the loss of orthogonality in time dispersive channels and to make an OFDM signal robust to time dispersion on the radio channel. As illustrated in FIG. 3, cyclic prefix insertion is performed by copying the last portion of the OFDM symbol and inserting it at the beginning of the OFDM symbol.
Cyclic prefix insertion is beneficial in the sense that it makes an OFDM signal robust to time dispersion as long as the span of the time dispersion does not exceed the length of the cyclic prefix. The drawback of cyclic prefix insertion is that only a fraction Tu/(Tu+TCP) of the received signal power is actually utilized by the OFDM demodulator. Cyclic prefix insertion also reduces the OFDM symbol rate from 1/Tu to 1/(Tu+TCP).
At the receiver side, the samples corresponding to cyclic prefix are discarded before FFT processing. Assuming a sufficiently large cyclic prefix, the linear convolution of a time dispersive radio channel will appear as a circular convolution during the OFDM symbol interval Tu. The combination of OFDM modulation (Inverse FFT (IFFT) processing), a time dispersive radio channel, and OFDM demodulation (FFT processing) can then be seen as a frequency domain channel as illustrated in FIG. 4, where the frequency domain channel taps h0, . . . , hN-1 can be directly derived from the channel impulse response, where N is the number of subcarriers used in an OFDM symbol.
The output rn,k of the kth subcarrier at the receiver in FIG. 4 is the transmitted modulation symbol xn,k scaled and phase rotated by the complex frequency domain channel tap hk and impaired by noise nk. To properly recover the transmitted symbol for data demodulation and channel decoding, the receiver should multiply rn,k with the complex conjugate of estimated channel, ĥk, as illustrated in FIG. 5. This is often referred as a one tap frequency domain equalizer being applied to each received subcarrier.
To perform data demodulation, the receiver has to estimate the frequency domain channel taps h0, . . . , hN-1. The frequency domain channel taps can be estimated by first estimating the channel impulse response and then converting it into frequency domain to estimate h0, . . . , hN-1. However, frequency domain channel taps may be estimated directly by using known reference symbols, which are inserted by the transmitter at regular intervals within the OFDM time-frequency grid, as illustrated in FIG. 6. The reference symbols are often referred as pilot symbols. The subcarrier on which the pilot symbol is transmitted is referred as pilot subcarrier. The terms pilot, pilot subcarrier, and pilot symbol are used interchangeably herein.
Using a priori information about the reference symbols, the receiver can estimate the frequency domain channel around the location of the reference symbols. The reference symbols should have a sufficiently high density in both the time and the frequency dimensions to be able to provide estimates for the entire time-frequency grid in a variety of channel conditions including radio propagation channels subject to high frequency and/or time selectivity. Different algorithms may be used for the channel estimation, such as averaging, linear interpolation, Minimum Mean Square Error (MMSE) estimation, etc. Some of these algorithms may require knowledge of the channel statistics.
There are several traditional methods for performing channel estimation. One of the commonly used methods is the MMSE channel estimation. In this method the known channel estimates from the surrounding pilot positions are used to form a MMSE channel estimate for data subcarriers. The pilots may be used from past and present OFDM symbols. Pilots from future OFDM symbols may also be used if storage and delay are not issues in an application. FIG. 7 illustrates an example of the MMSE channel estimation that uses seven pilots that are closest to the data symbol for which the channel estimate is needed.
Let (n, m) denote a data symbol position on OFDM symbol number n and subcarrier m. In FIG. 7, the initial available channel estimates for estimating a channel at position (9, 7) are the ones at the set of pilot positions as follows:Set—1={(4,5),(4,9),(8,4),(8,8),(8,12),(12,7),(12,11)}
Using the channel estimates at the above positions a two dimensional (2D) channel estimate is performed using a filter whose coefficients are computed according to MMSE criteria using the joint time and frequency correlation of the propagation channel. For example, to compute the channel estimate at data symbol position (9, 7) the coefficient that multiplies the pilot channel estimate at position (4, 5) is proportional to the channel correlation between the position of the pilot (4, 5) and the position of the data symbol (9, 7) whose channel estimate is desired. Similarly, the filter coefficient that multiplies the pilot channel estimate at position (8, 8) is proportional to the channel correlation between the position of the pilot (8, 8) and the position of the data symbol (9, 7) whose channel estimate is desired. For correlated propagation channels clearly there is a stronger channel correlation between positions (8, 8) and (9, 7) compared to correlation between positions (4, 5) and (9, 7). Therefore, depending on signal conditions, typically the pilot channel estimate at position (8, 8) is emphasized heavily in the channel estimation for position (9, 7). For each position within the 2D time-frequency grid, there will be a different set of filter coefficients. However, since the pilot pattern is repetitive, after four OFDM symbols, the same set of filter coefficients will be needed.
The above described MMSE channel estimation method uses pilots from different OFDM symbols and from different subcarriers in those OFDM symbols and therefore it is referred herein as 2D MMSE channel estimation. The 2D MMSE exploits the channel correlation that is typically present along both the time axis and the frequency axis. This type of MMSE estimation is often too complex and therefore lower complexity versions that provide performance close to that of a 2D MMSE estimation are developed in literature. Separable 2D MMSE estimation is one example of commonly used lower complexity channel estimation method. In this method, first the MMSE estimation is performed in one dimension based on the channel correlation in that dimension and then second MMSE is performed in another dimension which in turn exploits the correlation in that dimension.
The channel correlation along the time and frequency axis can be estimated based on the propagation channel models. Often the time and frequency correlation of the channel can be treated independently and therefore the channel estimation methods that exploit the channel correlation can also be separated. FIG. 8 illustrates an example of a separable 2D channel estimation procedure where 1D filtering is performed along time axis first and then the next 1D filtering is performed along frequency axis. The pilot symbols used in 1D filters along each axis is limited to the pilots available along the axis for which the filtering is being performed. FIG. 9 illustrates the pilots available for 1D filtering along the frequency axis.
There is a tradeoff between the density of pilots and the overhead in terms of portion of the total bandwidth and portion of the total power used up by the reference symbols such as pilots or training symbols. Although greater density of pilots is desirable for improved channel estimation, it takes away portion of the total bandwidth and portion of the total power that could otherwise be used for payload data transmission.
Mobile wireless communication systems operate under very dynamic propagation channel conditions. The propagation channel conditions between the transmitter and the receiver can vary rapidly because of the fast movement of the mobile terminals. Normally in mobile wireless communication systems a larger number of reference symbols are embedded in the transmitted signal to enable receivers to reliably estimate the rapidly varying channel conditions.
Once a communication system is designed with specified reference symbols information, the channel estimation methods in the receiver must be designed to take full advantage of the available reference symbols embedded in the transmitted signal.
In order to reduce the overhead of the reference symbols, some communication systems transmit the reference symbols at the beginning of a connection and then switch to payload data transmission. In this type of scenario, the receiver uses the initial reference (training) symbols to estimate the channel and then use this estimated channel for equalizing data symbols received during payload data transmission mode.
In many communication systems the channel varies over a period of time. Therefore it is necessary for the receiver to continuously track the changes in the channel and adapt the estimated channel. A common approach to track the channel variation is to use the demodulated data symbols as reference symbols for estimating the channel for the next symbol. This is often referred as Decision Directed Channel Estimation or Decision Feedback Equalization (DFE). The DFE uses the previously demodulated and/or decoded data symbols for estimating the channel for the present data symbol.
In OFDM systems, each OFDM symbol consists of a large number of subcarriers that are individually modulated. Some of these subcarriers may be designated as pilots and the modulation information for those subcarriers may be known a priori. In the absence of pilots in the present symbols, the demodulated data symbols from previous OFDM symbol may be used for estimating channel for the present symbol.
While such channel estimation techniques may provide an acceptable level of performance, it is desirable to provide improved channel estimation performance while reducing or keeping the same overhead in terms of bandwidth and power allocated to reference symbols. This is especially significant for receivers in highly mobile propagation environment.